Also how you describe Norfolk (my MC lives in Scotland which is fighting against England) is how I envisaged Scotland.
You might find a few ideas or even answers in Scottish history.
The big problem for the Scottish kings was that large chunks of what is now Scotland were frequently in the hands of other powers (not least the Norwegians in the early days) and they often only exerted nominal control over much of the rest.
Geography was one of the big reasons for this and probably would still be in your post apocalyptic world. You'll correct me if I'm wrong, but I have it in mind that about 80% of the population of modern Scotland lives in the central belt. The most productive agricultural land is the Merse, which runs down to the English border (you will know this but some other posters might not).
So, our post-apocalyptic king is likely to be stuck on Edinburgh rock, doing his best to keep the Merse in Scottish hands. You've told us he is at war with the perfidious English, so presumably Berwick is once again a target.
From Edinburgh, our king can exert direct control over the central belt and the eastern lowlands. In population terms, this gives him direct control over most of the people, but only a minority of the landmass. His whole border is a flashpoint, but history tells us that most invaders will avoid the mountainous centre and will come across the Merse (from Berwick or Newcastle) or across the Solway plain in the west (from Carlisle). So, our chap needs an ally in Dumfriesshire who can perhaps also act as a buffer against whoever is holding Galloway.
North of the central belt is that beautiful, but impenetrable and largely unproductive, landscape of shortbread tin fame. Our chap cannot waste his precious resources on holding down the north and the islands, but neither does he want them acting against him. So perhaps he offers virtual autonomy for the Highlands and Islands in exchange for tribute - possibly goods in kind, but otherwise levies of men for the English wars.
Yeah, the king in my story reverts to old Scottish money (which is almost the same as old English money) but paper. (I might use plastic or some other durable form.
Of course, money is only accepted where the king's writ runs. Trying to buy food in Wester Ross with lowland money which has no intrinsic value would be pretty futile. So perhaps the king tries to issue proper silver coinage, so the money has an actual value which will encourage wider usage?
You can have some real fun with this - let us know how you get on!
Regards,
Peter